00869nas a2200145 4500008004100000245003700041210003600078260001500114300001100129490000700140520049800147100002300645700001800668856003700686 2012 eng d00aLevinson's theorem for graphs II0 aLevinsons theorem for graphs II c2012/11/21 a1022070 v533 a We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n
semi-infinite paths each attached to a different vertex, generalizing a
previous result for the case n=1. This theorem counts the number of bound
states in terms of the winding of the determinant of the S-matrix. We also
provide a proof that the bound states and incoming scattering states of the
Hamiltonian together form a complete basis for the Hilbert space, generalizing
another result for the case n=1.
1 aChilds, Andrew, M.1 aGosset, David uhttp://arxiv.org/abs/1203.6557v2